Wideband Compressed Sensing Using Wavelet Packet Adaptive Reduced-set Matching Pursuit

One of the unsolved challenges in cognitive radio networks (CRNs) is the inability to sense a wideband spectrum in real-time. Traditional techniques require the use of analog-to digital converters (ADCs) of very high sampling rate, given by the Nyquist theorem. Recently, compressed sensing has presented itself as an efficient solution for spectrum sensing aiming to reduce such requirement. However, the complexity and speed of traditional compressed sensing recovery algorithms not particularly developed for CRNs prevented such an application. In this paper, we present the Wavelet Packet Adaptive Reduced-set Matching Pursuit (WP-ARMP) approach for compressed wide band spectrum sensing. WP-ARMP is a fast and accurate greedy recovery algorithm for compressed sensing, which is suitable for real-time CRN applications. Furthermore, we exploit the sparsity of the spectrum in the wavelet packet domain. Simulation results show that our technique can reconstruct spectrum signals from samples collected at 1/4 the Nyquist sampling rate. The proposed scheme is not only much faster than other related techniques, but also results in over 99% probability of detection and a probability of false alarm below 1%.